To some extent values of exponent k are available from various national studies of seismic hazard that give good source for cross validation of results.
Considering the most active seismic zone in Europe (based on results of SHARE study [2]) – the Vrancea intermediate depth seismic zone, national studies of exponent k known to authors are available for Romania and Bulgaria.
Seismic hazard analysis for Romania [3] deals in some detail with this topic as it gives separate figures for exponent k for national study and SHARE study. For the national study the determination range of exponent k was between 30 and 2475 years, which is somewhat different than in SHARE study, but not in a way that could compromise comparison of results. This paper showed that in SHARE study Vrancea source zone total territory coverage with maximum exponent k is much smaller compared to the national study.
Seismic hazard study of Bulgaria [4] showed values of exponent k ranging from 1.6 to 4.8, the latter being controlled by the Vrancea intermediate seismic hazard zone. The maximum values of exponent k obtained in national study are much higher than the ones in SHARE study [2] where this part of northern Bulgaria has values of exponent k of approximately 2.2. The high values of exponent k in national study also cover significant part of northern border zone with Romania.
For Italy, seismically active country that should be representative for recommended value of exponent k given in EN 1998-1, interactive results of seismic hazard are available online via INGV service [5], which can be used for determination of exponent k. For 50% percentile, and available range of data that correspond to return periods between 30 and 2500 years, the values of exponent k in areas of highest hazard are of the order of 2.5 which is similar to results in this study. Considering Table 1, the difference of importance factors for categories III and IV is 3% and 7%.
It is interesting to compare studies in areas with lower seismic hazard to the results of this study. For countries where no separate published studies on exponent k were found, we used values of importance factors in National Annexes for comparison. For instance, in Norwegian National Annex for EN 1998-1 [6] values of importance factors of 0.7, 1.0, 1.4 and 2.0 correspond to value of exponent k approximately 1.5, which is in good correlation with results of this study based on SHARE data (Table 2). Sweden has not yet issued national annex for EN 1998-1, but in study [7] exponent k is calculated for the city of Lund where value of 1.4 is obtained, which is similar to results in this study (Fig. 5). On the other hand, Germany [8] – left recommended values of importance factors in their National Annex although the seismic activity should lead to much higher importance factors. For example, the values of importance factors for the city of Cologne (Table 2) are thus underestimated by 16% and 32% for importance classes III and IV. Likewise, National Annex for France [9] leaves to the municipal authorities to determine values of importance factors, not mentioning that the values of exponent k dictate values of importance factors – i.e., that it is not purely political decision. From [10] it seems that single categorization is used for the entire country of France. United Kingdom [11] used base map for 2500 years and importance factor of 1.0, but in cases where TNCR is determined on a project – specific basis, the importance factor should be determined as well.